Yeah Pokémon distribution would be nice...
...but then again, it's just no fun anymore if everyone could just easily "create" their own army of "perfect" Pokémon...

Theoretically though, it shouldn't be impossible to set up the Wii as a Mystery Gift distribution system, unless the DS games use good signing/encryption, which I doubt. Emulating the DS is certainly not necessary for this, but the (probably game-specific) protocols must be reverse-engineered first.
I have no idea though how to spoof communications between the Wii and the DS, which must be done before any homebrew Wii-DS communication can be set up. If I understand it correctly, the Wii creates a private WLAN network with the DS when communicating, and the data is always sent directly (not via a router). So it's probably very hard to monitor such traffic...

I can't believe the idiocy I've seen on some of the
closed DS emulator for WII threads! People saying
shit like "Impossible" and "You'd need 3 hands!"

First off, there is a DS emulator for WII being worked
on. It's called ADS beta 0.1. http://wii.ds-scene.net/?s=viewtopic&nid=4475
SECONDLY... The DS's screen res is fuckin' small as hell.
Well enough to fit 2 square screens on 1 640x480 WII screen.
As for the speed, DESMUME is constantly updated and has PPC
builds released on a regular basis that work on WII LINUX.
I worked on the MIIGHT Linux for WII project (I did the V.I.C.E. port)
and remember running DESMUME for shits and giggles back then
and it ran fairly decent. I just can't believe all the naysaying.
I can't stand more than anything people who know nothing saying
something can't be done. The word can's shouldn't fuckin' exist in a
coder's vocabulary. And as for emulating the DS on the WII it isn't
like it's even that difficult! If you're going to say can't you should
at least apply it to something theoretically impossible!
I use DESMUME on the PC and it runs beautifully - there is no problem
with using a mouse for the stylus. A WIIMOTE could be even easier but
I'm not going to waste any more time discussing how stuff that can and
will be done can and will be done. Just wait or do it yourself.
Hell, load up DESMUME on any of the Linuxes that exist on WII and it
comes right up and runs fairly decent and that was half a year ago!
I have not sen ADS yet but I suspect it will only be a matter of time
before it's playable.